7. Coding and Modulation. FER-Zagreb, Satellite communication systems 2011/12

Transcription

1 7. Coding and Modulation

2 Topics Introduction Convolutional coding Reed-Solomon coding Concatenated coding FEC Forward error correction Digital modulation PCM Pulse code modulation QAM Quadrature amplitude modulation ISI intersymbol interference Modulation spectral efficiency BER bit error rate 1

3 Introduction Coders are part of transmitter systems and decoders are part of receiver systems. Signal transmission is subject to error or interference. There are error detecting and correcting codes. Parity (redundant) bits are introduced into the known information bits. This reduces the data speed. The number of parity bits necessary depends on interference in the communication channel and interference. Adequate decoder must exists on receiver side. Decoder depends on the coding method used on transmitter side. 2

4 Introduction In modulation process, one or more parameters of the auxiliary signal is changed. The auxiliary signal is called the carrier. Signal which contains the information is called the modulation signal. It controls the changes of carrier. The result of modulation procedure is modulated signal. Whole procedure is performed in modulator. Reverse procedure to modulating is demodulating at receiver. Difference between analog and digital modulations is in the modulation signal. With digital modulations, modulation signal is either 0 or 1. 3

5 Convolutional coding Code has three main characteristics: Code length number of bits in a code word Code dimension number of information bits in a code word Code distance number of bits necessary to move from one to other code word Convolutional coding can correct error bits which gives coding gain to the system. Codes have three parameters: n number of output bits k number of input bits m number of memory registers Ratio k/n = R is a code rate 4

6 Convolutional coding Usually k and n have values between 1 and 8, and code rate R has values from 1/8 to 7/8. There can be 2 to 10 memory registers (m). K is the number of bits in coder memory which affects the creation of n output bits: K = k (m - 1) Convolutional coding is performed with shift registers (K ) and n modulo 2 adders. Larger K means more influence of the previous bits on the output code word. Example K = 3, n = 2 For every bit in register, the output changes n = 2 code bits (u 1 and u 2 ) Code rate k/n = 1/2 Every output bit is a function of input bit (left state of register) and two previous bits (right states of register). 5

7 Convolutional coding Input bit m First code bit Second code bit Output word K = 3, n = 2 6

8 Convolutional coding Viterbi Decoder Viterbi decoder corrects the errors received during transmission. Decoding is more complicated procedure than encoding and limits the communication speed. Integer number K is the number of frames processed in every step. Input to decoder can be Real number (positive real number is logical zero and negative real number is positive one) 0 i 1 -hard decision soft decision integer between 0 and 2 b -1; b is a parameter of soft decision 7

9 Convolutional coding Decision for b = 3 Input value Decision 0 Most probable zero 1 Second most probable zero 2 Third most probable zero 3 Least probable zero 4 Least probable one 5 Third most probable one 6 Second most probable one 7 Most probable one 8

10 Convolutional coding Table shows typical values of decoding gain Code rate ρ E B /N 0 required for BEP = 10-6 (db) Decoding gain (db) / / / /

11 Reed-Solomon coding As convolutional coding, RS coding adds redundant bits and creates code words which enable correcting errors in decoder. Difference from convolutional coding is that RC encodes bit blocks instead one bit. RS coding is eight times more faster than convolutional coding. Input bits are first packed into small blocks of k symbols which are then packed in super blocks with n symbols by adding redundant bits. Transmission of information is decreased by code rate R, 1/R = n/k where n is number of output bits k is number of input bits RS decoder can correct t symbols of the code word according to 2t = n -k 10

12 Reed-Solomon coding RS(204,188, T=8) has 16 redundant bits and possibility to correct 8 bits. 2t = n k = = 16 t = 8 One bit is used for synchronization and 187 bits contain information. RS(204,188, T = 8) is shortened code from original RS(255, 239, T = 8). Used in DVB-S. 11

13 Concatenated coding Concatenated (joined) coding for DVB-S standard has two codes: outer (RS) and inner (convolutional). Inner decoder corrects errors at the output of demodulator, while outer decoder corrects occasional bursts of errors created by inner decoder. 12

14 FEC Forward Error Correction FEC is a digital signal processing which increases the reliability of data by introducing known structure into data stream before transmission. The known structure enables the receiving system detection and possible correction of errors in the channel or receiver. Correction of data means that it is not necessary to send the information again (useful with real time information). Original data is consisting of n bits. Encoder introduces redundant (parity) bits r, increasing total number of bits to n + r of code word. On the receiving end, decoder extracts the original data. The code rate is defined as ρ = n n + r where r is the number of redundant bits added to n information bits. 13

15 FEC Forward Error Correction The bit rate at the encoder input is R b. At output, the rate is greater and equal to R c : R = c Rb ρ 14

16 FEC Forward Error Correction Information...010I011I ,3 encoder Code word I I I Parity bits Information bits 15

17 FEC Forward Error Correction Digital Information input d 1, d 2,..., d k n, n+r encoder u 1, u 2,..., u k modulator noise Information bits Code bits channel Digital d 1, d 2,..., d k n, n+r u 1, u 2,..., u k Information decoder output demodulator Information bits estimation Code bits estimation 16

18 FEC Forward Error Correction Code measure is redundancy, or r/n. Codes with high redundancy have relatively little information per code bit. Codes with little redundancy have fast code rate (close to 1) and carry more information per code bit. High redundancy has advantage that it lowers the possibility of losing the original data during transmission. Disadvantage of high redundancy is that usually requires larger bandwidth or introduces delay. For the communication in real time, code rate must be increased by factor 1/(n+r) to avoid decrease in data throughput. Furthermore, it is necessary to increase the bandwidth by factor n/n+r (for modulation). If communication is not in real time, delay can be introduced but not the increased bandwidth. 17

19 FEC Forward Error Correction Quality parameter BER (bit error rate) vs ratio of S/N waterfall. When S/N increases, BER decreases system performs better Coded system (on figure) has 100 times smaller BER in comparison to the non coded system for same S/N. Or, coded system has same BER as non coded for lower S/N. Te difference is called coding gain (4 db in figure). Smaller necessary S/N needs smaller antennas, lower transmitting power, cheaper receivers,... BER Coding gain 8 12 non coded coded Direction of improvement regarding errors S/N [db] 18

20 Digital modulation ASK Amplitude Shift Keying With ASK, the amplitude of carrier is changed according to the modulation signal in a way that the carrier exists when modulation signal is equal to 1 and it does not exists if modulation signal is equal to 1. This modulation is also called OOK (On-Off Keying). Modulated signal is obtained by modulating the carrier signal (with frequency f c ) with modulating signal with frequency f m ): uask ( t) = Ucm cosωct + cosωmt cos3 ωmt π 3π Ideal ASK has infinitive spectrum. It is therefore necessary to shape pulses to narrow the frequency bandwidth. Disadvantage of ASK modulation is that S/N ratio is not same for 1 and for 0. It also needs different powers for those two states. Break in communication is read as 0. 19

21 Digital modulation ASK Amplitude Shift Keying 20

22 Digital modulation FSK Frequency Shift Keying With FSK, the frequency of carrier is changed discretely according to the modulation signal. The simplest FSK is the BPSK or binary FSK with two carrier frequencies. Examples: MSK Minimum Shift Keying with modulation index of 0.5 GMSK Gaussian MSK (mobile telephony) FSK modulation can be achieved with two ASK signals, having frequencies 1 f i 2 f. Demodulation of ASK is much easier than demodulation of FSK. 21

23 Digital modulation Modulation index is equal to the ratio of frequency deviation f and modulation frequency f m f mf = f Frequency deviation is f f f = m f 0 = f c - f f 1 = f c + f f c carrier frequency FSK Frequency Shift Keying 22

24 Digital modulation PSK Phase Shift Keying With PSK, the phase of carrier is changed in regard to the modulation signal. The modulation phase can have two or more different, previously determined phases. PSK modulation can also be obtained by two ASK signals, similar to FSK. The difference is that with PSK, this two signals must be in quadrature relation. PSK signal is equal to upsk ( t) = Ucm cos( ωct+ ϕm ) = Ucm [ cosϕm cosωct sinϕm sinωct] ϕ m is modulation phase which can be π ( 2n+ c) ϕm =, n= 0,1,2,... M 1; c= 0,1. M For M = 2, and c = 0, modulation phases will be 0 and π, and for c = 1, phases will be π/2 and 3π/2. This modulation is called BPSK or Binary PSK. Usually 0π or 0 represents state 1 and π or 180 represents 0. 23

25 Digital modulation PSK Phase Shift Keying 24

26 Digital modulation BPSK QPSK Gray code ( ) ( ) uqpsk t = I t cos ωct Qt ( )sin ωct. BPSK is resilient to interference but has small spectral efficiency. For M = 4, there are 4 modulation phases making QPSK. Each state of QPSK requires two bits while BPSK requires one bit. QPSK demands more memory, and the possibility of error is higher. Spectral efficiency is higher, that is, it is possible to transmit two times more information in a communication channel. 25

27 PCM Pulse Code Modulation With PCM modulation, amplitude of analog signal is sampled and quantized in order to realize binary code. PCM requires AD converter. The speed of sampling must be at least two times larger than the analog frequency: f s >= 2f c Quantization level will determine the accuracy of analog signal. Mode accurate conversion requires more memory. Demodulation is similar to modulation. Receiver needs DA converter. 26

28 QAM Quadrature amplitude modulation QAM is a procedure where the amplitudes of two carriers are modulated. The phase difference between them is 90. QAM can be both analog and digital. Analog QAM is similar to AM. Digital QAM is used more often than analog QAM. It has two modulation signals I(t) and Q(t) which are in relation ( ) ω ( ) uqam = Itcos ct Qtsin ωct. QPSK is actually a special case of QAM. Difference is that QPSK has no amplitude modulation while QAM has. Depending on the quantization level, there could be 4-QAM, 16-QAM, 64- QAM. More states means more possibility of error. 27

29 QAM Quadrature amplitude modulation 28

30 ISI Intersymbol interference When rectangular pulses pass through the frequency band limited channel, they spread in time, and pulse from each symbol will be spread into the time interval of adjacent (next) pulse. This leads to intersymbol interference. ISI can also appear from multipath propagation. The obvious solution for lowering ISI is increasing the frequency bandwidth. 29

31 ISI Interymbol interference Modern communication systems are working with minimum bandwidth. Unwanted emission outside bandwidth should be 40 db to 80 db lower than in its own channel. Since it is difficult to achieve it in RF band, pulse shaping is done in baseband or at MF. Figure shows frequency response (above) and impulse response (below) of raised-cosine filter with various roll-off factors. 30

32 Modulation spectral efficiency Modulation spectral efficiency is ratio of the transmitted bit rate R c and bandwidth occupied by the carrier. The bandwidth occupied by the carrier depends on spectrum of the modulated carrier and filtering. Filtering is used for lowering the interference to adjacent carriers. ISI-free transmissions can be achieved with raised cosine filter. Roll-off factor α will determine the bandwidth. For a raised cosine filter, the bandwidth B occupied by the carrier is: where T S is the symbol duration ( + α )/ T ( Hz) 1 S Spectral efficiency for M-ary modulation is equal to Γ = R B c = R T c B S = = log ( 1+ α ) ( 1+α ) ( bit/s/hz) For roll off factor α = 0.35, required bandwidth is 1.35/T S, and spectral efficiencies (bit/s/hz) are: 0.7 for BPSK, 1.5 for QPSK and 2.2 for 8PSK. 2 M 31

33 BER bit error rate Analog communications mostly use mean signal over mean noise (S/N) as a quality parameter. In analog communications, waveform can be imagined as signal with infinitely long duration and not divided in time, therefore with unlimited amount of energy. It has final mean power and infinitive energy. Therefore power is useful parameter for analog communications. With digital communications, symbols are transmitter in a part of time T S. If only one symbol is observed, mean power in all the time interval approaches zero. Therefore, power is not a satisfactory parameter for digital systems. In digital communications, more often is used E b /N 0, or normalized version of signal and noise: S N E = N b 0 R B where E b is energy per bit, N 0 is thermal noise in 1 Hz bandwidth, R is the data speed in the system and B T is the frequency bandwidth. T 32

34 BER bit error rate Symbol energy, or power integrated in time T s is much more useful parameter describing digital wave form. Eb J Ws = N = W/Hz Ws 0 Important characteristic of digital communication systems is BER, or number of bit errors in regard to E b /N 0. Larger E b /N 0 means smaller BER. System is adequate if BER is at least

35 BER bit error rate Bit error rate (BER) measures performance of demodulator by counting the number of bits in error, n in a stream of N received bits: BER = n/n BER constitutes a n estimate of the bit error probability (BEP). A level of confidence is associated with this estimate, as follows: n BEP = BER ± k N 63% level of confidence is obtained for k = 1 and 95% for k = 2. If n=100 errors within N = bits, BEP = 10 ± 10 with 63% confidence. Carrier phase (phase shift) changes under the influence of noise lead to errors in identification of received symbols, and bits. Symbol error probability (SEP) is probability of a symbol being detected in error (bit error probability is the probability of bit being detected in error). For two state modulation BEP = SEP, but for four state modulation, where phase states follow Gray code, BEP = SEP/2. In general BEP = SEP / log2 M form 2 34

36 BER bit error rate Figure shows theoretical bit error probabilities (BEP) for different modulations. Bit error rate (BER) measures performance of demodulator by counting the number of bits in error, n in a stream of N received bits: BER = n/n 35